diff --git a/Analysis/MeasureTheory/Section_1_1_2.lean b/Analysis/MeasureTheory/Section_1_1_2.lean index d13a3dba7..ff41aa168 100644 --- a/Analysis/MeasureTheory/Section_1_1_2.lean +++ b/Analysis/MeasureTheory/Section_1_1_2.lean @@ -660,15 +660,22 @@ lemma JordanMeasurable.measure_of_translate {d:ℕ} {E: Set (EuclideanSpace' d)} · exact eq_outer hE; /-- Exercise 1.1.7 (i) (Regions under graphs are Jordan measurable) -/ -lemma JordanMeasurable.graph {d:ℕ} {B:Box d} {f: EuclideanSpace' d → ℝ} (hf: ContinuousOn f B.toSet) : JordanMeasurable { p | ∃ x ∈ B.toSet, EuclideanSpace'.prod_equiv d 1 p = ⟨ x, f x ⟩ } := by +lemma JordanMeasurable.graph {d:ℕ} {B:Box d} (hB: IsClosed B.toSet) {f: EuclideanSpace' d → ℝ} + (hf: ContinuousOn f B.toSet) : + JordanMeasurable { p | ∃ x ∈ B.toSet, EuclideanSpace'.prod_equiv d 1 p = ⟨ x, f x ⟩ } := by sorry /-- Exercise 1.1.7 (i) (Regions under graphs are Jordan measurable) -/ -lemma JordanMeasurable.measure_of_graph {d:ℕ} {B:Box d} {f: EuclideanSpace' d → ℝ} (hf: ContinuousOn f B.toSet) : (JordanMeasurable.graph hf).measure = 0 := by +lemma JordanMeasurable.measure_of_graph {d:ℕ} {B:Box d} (hB: IsClosed B.toSet) + {f: EuclideanSpace' d → ℝ} (hf: ContinuousOn f B.toSet) : + (JordanMeasurable.graph hB hf).measure = 0 := by sorry /-- Exercise 1.1.7 (i) (Regions under graphs are Jordan measurable) -/ -lemma JordanMeasurable.undergraph {d:ℕ} {B:Box d} {f: EuclideanSpace' d → ℝ} (hf: ContinuousOn f B.toSet) : JordanMeasurable { p | ∃ x ∈ B.toSet, ∃ t:ℝ, EuclideanSpace'.prod_equiv d 1 p = ⟨ x, t ⟩ ∧ 0 ≤ t ∧ t ≤ f x } := by +lemma JordanMeasurable.undergraph {d:ℕ} {B:Box d} (hB: IsClosed B.toSet) + {f: EuclideanSpace' d → ℝ} (hf: ContinuousOn f B.toSet) : + JordanMeasurable + { p | ∃ x ∈ B.toSet, ∃ t:ℝ, EuclideanSpace'.prod_equiv d 1 p = ⟨ x, t ⟩ ∧ 0 ≤ t ∧ t ≤ f x } := by sorry /-- Exercise 1.1.8(i) (A triangle is Jordan measurable) -/